Copyright ©1997 by Paul Niquette. All rights reserved.
he statement in the puzzle, "You can drown in a lake the average depth of which is one foot" does not give a solver much information to work with. Many questions might go unanswered were it not for sophisticated instruments at our disposal called 'assumptions' (see Discovering Assumptions).
So for each unanswerable question ~~~ :
he resulting model of the matter is a cone-shaped lake with a non-swimmer thrashing around in the exact center. The average depth of a body of water can be obtained by dividing its volume by its surface area. The volume of a cone of radius R and depth D is given by
pi R2D / 3.
That's just one of those things sophisticated people know -- or else know how to find out.
Davg = (pi R2D / 3) / (pi R2),re you going to say it, or shall I? The disappearance of R in the equation means that the size of the lake does not matter. That takes care of assumption #6. But there's something else to get excited about, if you are so inclined. The deepest point in the lake is only...
You would have to be exceptionally short of stature or hopelessly clumsy to drown in that lake. That astonishing conclusion, we hasten to remind ourselves, results from the assumptions set forth above. Let's check them out.
How good are those assumptions?
A little research music, please...The first assumption is the most critical. If you can swim at all, then you need a deeper lake so that the water is over your head within the radius corresponding to your maximum swimming distance. But the lake does not have to be deeper than your height in just the exact center; accordingly, we might consider modifying assumption #5 so that there is a flat space on the lake bottom forming a water-filled cylinder of depth D that you can just barely swim halfway across.
Accordingly, however valid the principle may be, the declaration I have been using for five decades (see, for example, A Certain Bicyclist) is .
How would you correct the metaphor, "You can drown in a lake the average depth of which is one foot"? You might try a cylinder within a cylinder, but be prepared for another surprise.akes occur throughout much of the world, but they are most abundant in high latitudes and in mountain regions, particularly those that have been recently glaciated. They commonly occur along rivers with low gradients and wide flats and are associated with variations in the river channel. Many lakes are found in lowlands near the sea, especially in wet climates. That gives us some confidence in our assumption that lakes are shallower near their edges.
Lakes come in all sizes, but most have a surface area of about 100 square miles. Square miles? Lakes are not usually square, are they. A circular lake with a surface area of 100 square miles would have a diameter of about 11 miles. America has the world's largest freshwater lake in terms of surface area, but the Russians can claim the largest freshwater lake in terms of volume. If it were circular, Lake Superior, which covers almost 32,000 square miles, would be 200 miles across. Lake Baikal in Siberia holds 5,500 cubic miles of water. As a perfect cone 200 miles across, Lake Baikal would have an average depth of over 900 feet. How deep would it be at its center?
More of the world's lakes have been produced by glacial action than in any other way, but given enough run-off from rivers and melting snow you can have a lake in any depression that has an outlet above the lowest point. "Water seeks its own level," people like to say. How does it learn what that level is? I wonder.
Factors in lake-making include...
Viewed on the geological time scale, lakes are short-lived. Almost as soon as they are formed, three processes begin their destruction...
pl frustums or frusta [NL, fr. L, piece] (1658): the basal part of a solid
cone or pyramid formed by cutting off the top [or bottom] by a plane parallel
to the base [in this case the surface of the lake, which is (ahem) horizontal];
also: the part of a solid intersected between two usually parallel planes.
-- Merriam-Webster's Collegiate Dictionary